WILLIAMS.] 
FAUNAL DISSECTION OF THE DEVONIAN. 
59 
by the same man are, naturally, more likely to furnish correct com- 
parative statistics than lists made by different men. 
These three selected cases may be taken as offering a fair basis of 
reckoning, the results derived from which may constitute a fairly 
satisfactory standard, though they can not be regarded as final in 
any of the lists, since the statistics of the faunules are decidedly 
incomplete. This incompleteness of the fundamental statistics of 
this investigation, while important, does not invalidate the general 
conclusions which are drawn from them, for, although the exact degree 
of dominance is not mathematically expressed by the figures, or by 
the order of the species in the lists, the fact of dominance is clearly 
expressed for the species mentioned. 
In order to reduce to a minimum the errors pertaining to the sev- 
eral modes of measuring the bionic values of the species the average 
may be struck, and thus dominance of both kinds may be expressed 
in a final list which may stand as a standard and representative list 
of the dominant species of the Tropidoleptus carinatus fauna. 
In order to add together the statistics of various kinds regarding 
the same species the several fractions may be reduced to percentages 
(Table IV). The statistics are in three sets and are expressed in fig- 
ures at the right of the species tabulated in the preceding tables (I, 
II, III). The figures express the following facts: 
(1) The geographic frequency of occurrence of the species in the 
146 sample collections made in eastern New York and Pennsylvania. 
(2) The frequency of recurrence in the 25 zones making up the ver- 
tical column of the Cayuga Lake section. 
(3) The frequency of the vertical recurrence of the species in the 
35 zones of the Eighteenmile Creek section. 
The total number of stations in the first group is 146; the total num- 
ber of zones in the second group is 25; the total number of zones in 
the third group is 35. 
By reducing the fractions to approximate percentage values we get 
the following: table : 
Table IV. — Tropidoleptus fauna: Preliminary dominant list. 
Spirifer pennatns 
Tropidoleptus carinatus 
Spirifer granulosus 
Chonetes coronatus 
Palaeoneilo constricta „ . 
Nucula bellistriata 
Ambocoeria umbonata-- 
Nuculites triqueter 
N. oblongatus 
Nucula corbuliformis . 
Athyris spiriferoides _ . . 
Phacops rana 
Eastern 
New 
York. 
Per cent. 
78 
60 
40 
40 
40 
29 
28 
28 
24 
23 
22 
22 
Pavn™ Eighteen- 
tJvP mile 
Lake " Creek. 
Pei 
cent. 
80 
84 
40 
52 
84 
32 
84 
68 
64 
76 
68 
80 
Per cen t. 
80 
23 
29 
17 
12 

51 
3 
6 

60 
74 
Ontario, 
Canada. 
5. 
Totai. 
Per cent. 
238 
167 
109 
109 
136 
61 
163 
99 
94 
99 
150 
176 
Rank of 
species. 
1 
3 
7 
8 
6 
12 
4 
9 
II 
K) 
5 
2 
